It will keep for a little while. I think several days only. I have used alum after a week and a half and it was noticeably weaker. Alum oxidizes when it comes in contact with the air, so keeping the solution covered should make it last longer than leaving it open to the air.

The other things i suggest is that I have started using a much weaker alum solution for silk. It is 2 teaspoons of alum vs 2 tablespoons.

Thanks. My first effort with small silk habotai hankies was fairly successful, except that some color ran into a white area when I hung it up to dry. I had only dipped the fabric into the alum rather than soaking it. I've read that a 20 minute soak is recommended? Also, they're a little stiffer than I'd expected. I did a scrap piece if silk chiffon that came out feeling much nicer.

I'm having a little trouble now holding onto the color. If I rinse right away, the fabric looks faded. I read your recommendation to postpone rinsing until after the fabric has dried, but how do you prevent having some of the color run? Are you drying the fabric flat, or hanging to dry?

I hang to dry. Sometimes it looks like the color is running, but that layer of carrageenan actually protects it. You can dry flat to make sure its doesn't run. The other thing to do is that if the color is running, you have put more on than the fabric can handle. Back off a bit on the amount of color you add, and it should stick fine.